Partially Correlated Verifier Cascades in LLM Harnesses: Concave Log-Odds, Polynomial Reliability, and Blind-Spot Ceilings

arXiv cs.AI · 18 hours ago

Researchers developed a mathematical theory for partially correlated verifier cascades in large language models, showing that when multiple verifiers check an answer, the posterior log-odds grow concavely rather than linearly in the number of verifiers. For Beta-distributed latent variables, failure decays polynomially as k^(-b) rather than exponentially, and a blind-spot ceiling at mass 1-π prevents reliability from saturating below 1. Independence-based models underestimate failure by 20x at k=5 and 3000x at k=10, indicating that improving reliability requires decorrelating verifiers through different model families or evidence sources rather than simply adding more gates.